<p><b>Abstract</b>—The paper describes a framework for representing and reasoning with periodic events. In particular, it proposes a temporal formalism which deals with both 1) quantitative information concerning the frame of time (e.g., <it>between 1990 and 1993</it>) and the user-defined calendar-dates (e.g., <it>on the first Mondays of April</it>) in which periodic events are located and 2) the qualitative relations between periodic events (e.g., <it>Sam visits the branch office X01 before going to his office</it>). The meaning of the temporal specifications in our formalism is described in logical terms. The paper defines the basic operations of inversion, intersection and composition of temporal specifications. These operations are correct (with respect to the logical definition of the specifications) and do not lose information. Finally, the paper also describes a correct algorithm which takes advantage of these operations for performing temporal reasoning, and analyses its complexity. An application of the temporal framework to the scheduling in an office is shown in an example.</p>